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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

Von Neumann on measure and ergodic theory


Author: Paul R. Halmos
Journal: Bull. Amer. Math. Soc. 64 (1958), 86-94
MathSciNet review: 0097294
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References | Additional Information

References [Enhancements On Off] (What's this?)

  • 1. G. D. Birkhoff, Proof of the ergodic theorem, Proc. Nat. Acad. Sci. vol. 17 (1931) pp. 656-660.
  • 2. G. D. Birkhoff and B. O. Koopman, Recent contributions to the ergodic theory, Proc. Nat. Acad. Sci. vol. 18 (1932) pp. 279-282.
  • 3. B. O. Koopman, Hamiltonian systems and transformations in Hilbert space, Proc. Nat. Acad. Sci. vol. 17 (1931) pp. 315-318.
  • 4. John von Neumann, Die Zerlegung eines Intervalles in abzählbar viele kongruente Teilmengen, Fund. Math. vol. 11 (1928) pp. 230-238.
  • 5. John von Neumann, Zur allgemeinen Theorie des Masses, Fund. Math. vol. 13 (1929) pp. 73-116.
  • 6. John von Neumann, Zusatz zur Arbeit "Zur allgemeinen Theorie des Masses", Fund. Math. vol. 13 (1929) p. 333.
  • 7. John von Neumann, A numerical method to determine optimum strategy, Naval Res. Logist. Quart. 1 (1954), 109–115. MR 0063776 (16,178c)
  • 8. John von Neumann, Proof of the quasi-ergodic hypothesis, Proc. Nat. Acad. Sci. vol. 18 (1932) pp. 70-82.
  • 9. John von Neumann and B. O. Koopman, Dynamical systems of continuous spectra, Proc. Nat. Acad. Sci. vol. 18 (1932) pp. 255-263.
  • 10. John von Neumann, Physical applications of the ergodic hypothesis, Proc. Nat. Acad. Sci. vol. 18 (1932) pp. 263-266.
  • 11. J. von Neumann, Einige Sätze über messbare Abbildungen, Ann. of Math. (2) 33 (1932), no. 3, 574–586 (German). MR 1503077, http://dx.doi.org/10.2307/1968536
  • 12. J. von Neumann, Zur Operatorenmethode in der klassischen Mechanik, Ann. of Math. (2) 33 (1932), no. 3, 587–642 (German). MR 1503078, http://dx.doi.org/10.2307/1968537
  • 13. J. von Neumann, Züsatze zur Arbeit “zur Operatorenmethode...”, Ann. of Math. (2) 33 (1932), no. 4, 789–791 (German). MR 1503096, http://dx.doi.org/10.2307/1968225
  • 14. J. V. Neumann, Zum Haarschen Maß\ in topologischen Gruppen, Compositio Math. 1 (1935), 106–114 (German). MR 1556880
  • 15. John von Neumann and M. H. Stone, The determination of representative elements in the residual classes of a Boolean algebra, Fund. Math. vol. 25 (1935) pp. 353-378.
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  • 17. Israel Halperin, The extraordinary inspiration of John von Neumann, The legacy of John von Neumann (Hempstead, NY, 1988) Proc. Sympos. Pure Math., vol. 50, Amer. Math. Soc., Providence, RI, 1990, pp. 15–17. MR 1067747 (92e:01068), http://dx.doi.org/10.1090/pspum/050/1067747
  • 18. Paul R. Halmos and John von Neumann, Operator methods in classical mechanics. II, Ann. of Math. (2) 43 (1942), 332–350. MR 0006617 (4,14e)
  • 19. John von Neumann, Functional Operators. I. Measures and Integrals, Annals of Mathematics Studies, no. 21, Princeton University Press, Princeton, N. J., 1950. MR 0032011 (11,240f)


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9904-1958-10203-7
PII: S 0002-9904(1958)10203-7